相关论文: No vortex in straight flows -- on the eigen-repres…
In this paper, we study the evolution of a vortex filament in an incompressible ideal fluid. Under the assumption that the vorticity is concentrated along a smooth curve in $\mathbb{R}^3$, we prove that the curve evolves to leading order by…
Small-scale turbulence can be comprehensively described in terms of velocity gradients, which makes them an appealing starting point for low-dimensional modeling. Typical models consist of stochastic equations based on closures for…
One of the ubiquitous features of real-life turbulent flows is the existence and persistence of coherent vortices. Here we show that such coherent vortices can be extracted as clusters of Lagrangian trajectories. We carry out the clustering…
Entangled vortex filaments are essential to turbulence, serving as coherent structures that govern nonlinear fluid dynamics and support the reconstruction of fluid fields to reveal statistical properties. This study introduces an quantum…
The velocity gradient tensor can be decomposed into normal straining, pure shearing and rigid rotation tensors, each with distinct symmetry and normality properties. We partition the strength of turbulent velocity gradients based on the…
We derive an analytic formula for the hydrodynamic Green function and the Robin function on every orientable surface admitting a hydrodynamic Killing vector field. Closed-form expressions are provided for all fourteen canonical Riemann…
A single hydrodynamic vortex on a surface will in general moves unless its Riemannian metric is a special "Steady Vortex Metric" (SVM). Metrics of constant curvature are SVM only in surfaces of genus zero and one. In this paper: (1) I show…
An improved understanding of turbulence is essential for the effective modelling and control of industrial and geophysical processes. Homogeneous, isotropic turbulence (HIT) is the archetypal field for developing turbulence physics theory.…
In this paper a model for viscous boundary and shear layers in three-dimensions is introduced and termed a vortex-entrainment sheet. The vorticity in the layer is accounted for by a conventional vortex sheet. The mass and momentum in the…
In this paper, we study two-dimensional steady incompressible Euler flows in which the vorticity is sharply concentrated in a finite number of regions of small diameter in a bounded domain. Mathematical analysis of such flows is an…
We consider the motion of the interface separating two domains of the same fluid that moves with different velocity along the tangential direction of the interface. We assume that the fluids occupying the two domains are of constant…
Nondissipative force acting on a vortex in Fermi superfluids and superconductors is calculated from the spectral flow of fermion zero modes in the vortex core. The spectral flow effect casts a new light on the problem of mutual friction in…
Cross-flow, or vertical-axis, turbines are a promising technology for capturing kinetic energy in wind or flowing water and their inherently unsteady fluid mechanics present unique opportunities for control optimization of individual rotors…
A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of breaks (including shocks) is presented in the framework of an exact Clebsch type representation of the…
Consideration is given to the effects of inhomogeneous shear flow (both regular and chaotic) on nematic liquid crystals in a planar geometry. The Landau--de Gennes equation coupled to an externally-prescribed flow field is the basis for the…
How can we understand gradient-based training over non-convex landscapes? The edge of stability phenomenon, introduced in Cohen et al. (2021), indicates that the answer is not so simple: namely, gradient descent (GD) with large step sizes…
A three-dimensional round liquid jet within a low-speed coaxial gas flow is numerically simulated and explained via vortex dynamics ($\lambda_2$ method). The instabilities on the liquid-gas interface reflect well the vortex interactions…
The work reported below is a first of its kind study of the properties of turbulent flow without strong mean shear in a Newtonian fluid in proximity of the turbulent/non-turbulent interface, with emphasis on the small scale aspects. The…
The JHU turbulence database [1] can be used with a state of the art visualisation tool [2] to generate high quality fluid dynamics videos. In this work we investigate the classical idea that smaller structures in turbulent flows, while…
A rigorous method for introducing the variational principle describing relativistic ideal hydrodynamic flows with all possible types of discontinuities (including shocks) is presented in the framework of an exact Clebsch type representation…